# V=L x di/dt rearrangements?

by hobbs125
Tags: di or dt, rearrangements
 P: 104 V=L x di/dt is a well known formula used to calculate the voltage across an inductor due to a collapsing magnetic field. It seems to me that the formula could also be arranged to say: V = i x dL/dt Voltage is equal to current times the change in inductance... If this formula is true would a decreasing (collapsing) inductance produce an opposite polarity across the coil than an increasing inductance? if I wind two coils together and connect them in a series circuit so they oppose each other. When the pulse goes through the coils it would cause the inductance to change (drop to zero) and induce a voltage across the coil? Could the equation above then be used to calculate the voltage across the coil? Are there any applications where this is used?
P: 1,089
 Quote by hobbs125 It seems to me that the formula could also be arranged to say: V = i x dL/dt Voltage is equal to current times the change in inductance...

This is absolutely not true.

EDIT: Clearly I misunderstood something!
 Sci Advisor PF Gold P: 3,679 Absolutely true. Inductance is defined as flux(linkages) per ampere and the changing flux causes an EMF irrespective of whether it resulted from change in amps or change in inductance. That's why a solenoid creates a dip in the current as its airgap closes.
 P: 2,251 V=L x di/dt rearrangements? jim is right. i haven't seen this done with inductors, but i have seen it done with capacitors (in a Wurlitzer electric piano). in both cases, it's a consequence of the product rule of derivatives: $$i(t) = C(t)\frac{dv(t)}{dt} + v(t)\frac{dC(t)}{dt}$$ i think the counterpart for coils is: $$v(t) = L(t)\frac{di(t)}{dt} + i(t)\frac{dL(t)}{dt}$$
 P: 589 The explosively pumped flux compression generator is an example of this.
 P: 104 Jim Handy, That's exactly what I was thinking. And I don't see any reason why that rearrangement of the formula is wrong. The_emi_guy, Could this be done on a small scale using coils as I described above?

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